It really depends on the USB-C port on that laptop. If ASUS enabled DisplayPort over USB-C. Then the USB-C port would be the best option for a second monitor. As you could use a USB-C to HDMI, DVI or DisplayPort cable for a direct connection to your internal graphics.
If they did not enable DisplayPort over USB-C. Then it would not matter if you used a USB-C or USB-A adapter. As both are USB 3.1 Gen 1. This second type of adapter is actually a low end GPU and costs significantly more than a simple cable. These adapters tend to be a bit laggy. USB-A is likely the better option in this scenario as there are simply more adapters on the market. Although you could use a USB-C dock. Just make sure it is a USB-C dock and not a Thunderbolt 3 dock.
Unfortunately with the manual for the A571GD I found. It makes no mention I could find as to whether or not the USB-C port supports DisplayPort.
I'd suggest contacting technical support on the ASUS website for your laptop. To determine if the USB-C port supports DisplayPort. Also if your laptop supports dual external monitors. It should as the integrated and discrete graphics should be able to support three displays (1 internal + 2 external). It's just a matter of whether or not ASUS implemented that support.
ASUS website (tech chat should show up as a blue bubble):
https://www.asus.com/th/Laptops/A571GT/
Edit: Just to be clear. Use the HDMI port for one monitor. It's just a question of the second monitor as to what options are available.